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CholeskyDecomposition (Commons Math 3.2 API)
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org.apache.commons.math3.linear</FONT>
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Class CholeskyDecomposition</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.linear.CholeskyDecomposition</B>
</PRE>
<HR>
<DL>
<DT><PRE>public class <B>CholeskyDecomposition</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></DL>
</PRE>

<P>
Calculates the Cholesky decomposition of a matrix.
 <p>The Cholesky decomposition of a real symmetric positive-definite
 matrix A consists of a lower triangular matrix L with same size such
 that: A = LL<sup>T</sup>. In a sense, this is the square root of A.</p>
 <p>This class is based on the class with similar name from the
 <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the
 following changes:</p>
 <ul>
   <li>a <A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getLT()"><CODE>getLT</CODE></A> method has been added,</li>
   <li>the <code>isspd</code> method has been removed, since the constructor of
   this class throws a <A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear"><CODE>NonPositiveDefiniteMatrixException</CODE></A> when a
   matrix cannot be decomposed,</li>
   <li>a <A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getDeterminant()"><CODE>getDeterminant</CODE></A> method has been added,</li>
   <li>the <code>solve</code> method has been replaced by a <A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getSolver()"><CODE>getSolver</CODE></A> method and the equivalent method provided by the returned
   <A HREF="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear"><CODE>DecompositionSolver</CODE></A>.</li>
 </ul>
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>2.0 (changed to concrete class in 3.0)</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: CholeskyDecomposition.java 1416643 2012-12-03 19:37:14Z tn $</DD>
<DT><B>See Also:</B><DD><a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a>, 
<a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a></DL>
<HR>

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<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD">DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Default threshold below which diagonal elements are considered null
 and matrix not positive definite.</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD">DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Default threshold above which off-diagonal elements are considered too different
 and matrix not symmetric.</TD>
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<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix)">CholeskyDecomposition</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculates the Cholesky decomposition of the given matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix, double, double)">CholeskyDecomposition</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix,
                      double&nbsp;relativeSymmetryThreshold,
                      double&nbsp;absolutePositivityThreshold)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculates the Cholesky decomposition of the given matrix.</TD>
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<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getDeterminant()">getDeterminant</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Return the determinant of the matrix</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getL()">getL</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the matrix L of the decomposition.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getLT()">getLT</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the transpose of the matrix L of the decomposition.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear">DecompositionSolver</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#getSolver()">getSolver</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get a solver for finding the A &times; X = B solution in least square sense.</TD>
</TR>
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<A NAME="DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><!-- --></A><H3>
DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</H3>
<PRE>
public static final double <B>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</B></PRE>
<DL>
<DD>Default threshold above which off-diagonal elements are considered too different
 and matrix not symmetric.
<P>
<DL>
<DT><B>See Also:</B><DD><A HREF="../../../../../constant-values.html#org.apache.commons.math3.linear.CholeskyDecomposition.DEFAULT_RELATIVE_SYMMETRY_THRESHOLD">Constant Field Values</A></DL>
</DL>
<HR>

<A NAME="DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><!-- --></A><H3>
DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</H3>
<PRE>
public static final double <B>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</B></PRE>
<DL>
<DD>Default threshold below which diagonal elements are considered null
 and matrix not positive definite.
<P>
<DL>
<DT><B>See Also:</B><DD><A HREF="../../../../../constant-values.html#org.apache.commons.math3.linear.CholeskyDecomposition.DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD">Constant Field Values</A></DL>
</DL>

<!-- ========= CONSTRUCTOR DETAIL ======== -->

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<A NAME="CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix)"><!-- --></A><H3>
CholeskyDecomposition</H3>
<PRE>
public <B>CholeskyDecomposition</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix)</PRE>
<DL>
<DD>Calculates the Cholesky decomposition of the given matrix.
 <p>
 Calling this constructor is equivalent to call <A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix, double, double)"><CODE>CholeskyDecomposition(RealMatrix, double, double)</CODE></A> with the
 thresholds set to the default values <A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><CODE>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</CODE></A> and <A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><CODE>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</CODE></A>
 </p>
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>matrix</CODE> - the matrix to decompose
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</A></CODE> - if the matrix is not square.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSymmetricMatrixException.html" title="class in org.apache.commons.math3.linear">NonSymmetricMatrixException</A></CODE> - if the matrix is not symmetric.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</A></CODE> - if the matrix is not
 strictly positive definite.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix, double, double)"><CODE>CholeskyDecomposition(RealMatrix, double, double)</CODE></A>, 
<A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><CODE>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</CODE></A>, 
<A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><CODE>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</CODE></A></DL>
</DL>
<HR>

<A NAME="CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix, double, double)"><!-- --></A><H3>
CholeskyDecomposition</H3>
<PRE>
public <B>CholeskyDecomposition</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A>&nbsp;matrix,
                             double&nbsp;relativeSymmetryThreshold,
                             double&nbsp;absolutePositivityThreshold)</PRE>
<DL>
<DD>Calculates the Cholesky decomposition of the given matrix.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>matrix</CODE> - the matrix to decompose<DD><CODE>relativeSymmetryThreshold</CODE> - threshold above which off-diagonal
 elements are considered too different and matrix not symmetric<DD><CODE>absolutePositivityThreshold</CODE> - threshold below which diagonal
 elements are considered null and matrix not positive definite
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</A></CODE> - if the matrix is not square.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSymmetricMatrixException.html" title="class in org.apache.commons.math3.linear">NonSymmetricMatrixException</A></CODE> - if the matrix is not symmetric.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</A></CODE> - if the matrix is not
 strictly positive definite.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#CholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix)"><CODE>CholeskyDecomposition(RealMatrix)</CODE></A>, 
<A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_RELATIVE_SYMMETRY_THRESHOLD"><CODE>DEFAULT_RELATIVE_SYMMETRY_THRESHOLD</CODE></A>, 
<A HREF="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html#DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD"><CODE>DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD</CODE></A></DL>
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<A NAME="getL()"><!-- --></A><H3>
getL</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>getL</B>()</PRE>
<DL>
<DD>Returns the matrix L of the decomposition.
 <p>L is an lower-triangular matrix</p>
<P>
<DD><DL>

<DT><B>Returns:</B><DD>the L matrix</DL>
</DD>
</DL>
<HR>

<A NAME="getLT()"><!-- --></A><H3>
getLT</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</A> <B>getLT</B>()</PRE>
<DL>
<DD>Returns the transpose of the matrix L of the decomposition.
 <p>L<sup>T</sup> is an upper-triangular matrix</p>
<P>
<DD><DL>

<DT><B>Returns:</B><DD>the transpose of the matrix L of the decomposition</DL>
</DD>
</DL>
<HR>

<A NAME="getDeterminant()"><!-- --></A><H3>
getDeterminant</H3>
<PRE>
public double <B>getDeterminant</B>()</PRE>
<DL>
<DD>Return the determinant of the matrix
<P>
<DD><DL>

<DT><B>Returns:</B><DD>determinant of the matrix</DL>
</DD>
</DL>
<HR>

<A NAME="getSolver()"><!-- --></A><H3>
getSolver</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear">DecompositionSolver</A> <B>getSolver</B>()</PRE>
<DL>
<DD>Get a solver for finding the A &times; X = B solution in least square sense.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>a solver</DL>
</DD>
</DL>
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